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PTAS for ktour cover problem on the plane for moderately large values of k
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Adamaszek, Anna, Czumaj, Artur and Lingas, Andrzej. (2010) PTAS for ktour cover problem on the plane for moderately large values of k. International Journal of Foundations of Computer Science, Volume 21 (Number 6). pp. 893904. ISSN 01290541
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Official URL: http://dx.doi.org/10.1142/S0129054110007623
Abstract
Let P be a set of n points in the Euclidean plane and let O be the origin point in the plane. In the ktour cover problem (called frequently the capacitated vehicle routing problem), the goal is to minimize the total length of tours that cover all points in P, such that each tour starts and ends in O and covers at most k points from P.
The ktour cover problem is known to be NPhard. It is also known to admit constant factor approximation algorithms for all values of k and even a polynomialtime approximation scheme (PTAS) for small values of k, k = circle divide (log n/ log log n).
In this paper, we significantly enlarge the set of values of k for which a PTAS is provable. We present a new PTAS for all values of k <= 2(log delta n), where delta = delta(epsilon). The main technical result proved in the paper is a novel reduction of the ktour cover problem with a set of n points to a small set of instances of the problem, each with circle divide((k/epsilon)(circle divide(1))) points.
Item Type:  Journal Article  

Subjects:  Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software 

Divisions:  Faculty of Science > Computer Science  
Library of Congress Subject Headings (LCSH):  Transportation problems (Programming), Approximation algorithms  
Journal or Publication Title:  International Journal of Foundations of Computer Science  
Publisher:  World Scientific Publishing Co. Pte. Ltd.  
ISSN:  01290541  
Official Date:  December 2010  
Dates: 


Volume:  Volume 21  
Number:  Number 6  
Page Range:  pp. 893904  
Identifier:  10.1142/S0129054110007623  
Status:  Peer Reviewed  
Publication Status:  Published  
Access rights to Published version:  Restricted or Subscription Access  
Funder:  Engineering and Physical Sciences Research Council (EPSRC), Sweden. Vetenskapsrådet [Research Council], University of Warwick. Centre for Discrete Mathematics and Its Applications  
Grant number:  EP/D063191/1 (EPSRC), 6212005408 (VR)  
Version or Related Resource:  Adamaszek, Anna, et al. (2009). PTAS for ktour cover problem on the plane for moderately large values of k. Lecture Notes in Computer Science, 5878, pp. 9941003. http://wrap.warwick.ac.uk/id/eprint/5481  
Related URLs:  
References:  [1] S. Arora. Polynomial time approximation schemes for Euclidean traveling salesman 

URI:  http://wrap.warwick.ac.uk/id/eprint/41591 
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